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Two buses travel on the same highway between Eastgate and Westhaven in opposite directions. Each bus travels at a constant speed. At the same time, one bus leaves Eastgate for Westhaven and the other leaves Westhaven for Eastgate. How many hours does the bus that leaves Westhaven take to reach Eastgate?
(1) The speed of the bus that leaves Eastgate is 2/5 of the speed of the bus that leaves Westhaven.
(2) The two buses pass each other 5 hours after they depart.
(1) The speed of the bus that leaves Eastgate is 2/5 of the speed of the bus that leaves Westhaven.
(2) The two buses pass each other 5 hours after they depart.
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27 Mar 2026, 01:00
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GMAT Club Official Solution:
Two buses travel on the same highway between Eastgate and Westhaven in opposite directions. Each bus travels at a constant speed. At the same time, one bus leaves Eastgate for Westhaven and the other leaves Westhaven for Eastgate. How many hours does the bus that leaves Westhaven take to reach Eastgate?
(1) The speed of the bus that leaves Eastgate is 2/5 of the speed of the bus that leaves Westhaven.
A speed ratio alone does not determine the travel time because the distance between Eastgate and Westhaven is unknown. Not sufficient.
(2) The two buses pass each other 5 hours after they depart.
Knowing only when they pass each other does not determine the full travel time because the buses’ speeds are unknown. Not sufficient.
(1)+(2) Let the Westhaven bus’s speed be v. Then the Eastgate bus’s speed is (2/5)v. In 5 hours, the Westhaven bus travels 5v and the Eastgate bus travels 5 * (2/5)v = 2v. Since they meet after 5 hours, the total distance is 5v + 2v = 7v. The Westhaven bus needs to travel that full distance at speed v, so its travel time is (7v)/v = 7 hours. Sufficient.
Answer: C.
Two buses travel on the same highway between Eastgate and Westhaven in opposite directions. Each bus travels at a constant speed. At the same time, one bus leaves Eastgate for Westhaven and the other leaves Westhaven for Eastgate. How many hours does the bus that leaves Westhaven take to reach Eastgate?
(1) The speed of the bus that leaves Eastgate is 2/5 of the speed of the bus that leaves Westhaven.
A speed ratio alone does not determine the travel time because the distance between Eastgate and Westhaven is unknown. Not sufficient.
(2) The two buses pass each other 5 hours after they depart.
Knowing only when they pass each other does not determine the full travel time because the buses’ speeds are unknown. Not sufficient.
(1)+(2) Let the Westhaven bus’s speed be v. Then the Eastgate bus’s speed is (2/5)v. In 5 hours, the Westhaven bus travels 5v and the Eastgate bus travels 5 * (2/5)v = 2v. Since they meet after 5 hours, the total distance is 5v + 2v = 7v. The Westhaven bus needs to travel that full distance at speed v, so its travel time is (7v)/v = 7 hours. Sufficient.
Answer: C.
General Discussion
18 Mar 2026, 23:28
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Classic two-trains (or buses) problem. The key is recognizing that neither statement alone gives you enough to find the actual travel time, but together they do.
Let D = distance between Eastgate and Westhaven.
Let v_W = speed of the bus leaving Westhaven.
Let v_E = speed of the bus leaving Eastgate.
We want: D / v_W (hours for the Westhaven bus to reach Eastgate).
1. Statement (1): v_E = (2/5) * v_W.
This tells us the ratio of speeds. But we still have two unknowns: D and v_W. No way to find D / v_W without more info. Not sufficient.
2. Statement (2): The buses pass each other 5 hours after departing.
When they meet, they've together covered the full distance D.
So: (v_E + v_W) * 5 = D.
But we don't know v_E or v_W individually, just their combined rate times 5. Not sufficient.
Together: From (1), v_E = (2/5)v_W. Plug into the equation from (2):
((2/5)v_W + v_W) * 5 = D
(7/5)v_W * 5 = D
7 * v_W = D
D / v_W = 7
The Westhaven bus takes 7 hours. Sufficient.
Answer: C.
The trap is thinking Statement (2) is enough because you get a number (5 hours). But that's the time until they meet, not the time for either bus to complete the trip. You need the speed ratio from (1) to figure out what fraction of the journey each bus has done at the meeting point.
Let D = distance between Eastgate and Westhaven.
Let v_W = speed of the bus leaving Westhaven.
Let v_E = speed of the bus leaving Eastgate.
We want: D / v_W (hours for the Westhaven bus to reach Eastgate).
1. Statement (1): v_E = (2/5) * v_W.
This tells us the ratio of speeds. But we still have two unknowns: D and v_W. No way to find D / v_W without more info. Not sufficient.
2. Statement (2): The buses pass each other 5 hours after departing.
When they meet, they've together covered the full distance D.
So: (v_E + v_W) * 5 = D.
But we don't know v_E or v_W individually, just their combined rate times 5. Not sufficient.
Together: From (1), v_E = (2/5)v_W. Plug into the equation from (2):
((2/5)v_W + v_W) * 5 = D
(7/5)v_W * 5 = D
7 * v_W = D
D / v_W = 7
The Westhaven bus takes 7 hours. Sufficient.
Answer: C.
The trap is thinking Statement (2) is enough because you get a number (5 hours). But that's the time until they meet, not the time for either bus to complete the trip. You need the speed ratio from (1) to figure out what fraction of the journey each bus has done at the meeting point.
